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2 years ago

One factor of mc018-1.jpg is (x + 7). What are all the roots of the function? Use the Remainder Theorem.

Mathematics

2 answers:

Inessa05 [86]2 years ago

4 0

Answer:

It’s b

Step-by-step explanation:

mezya [45]2 years ago

3 0

One factor of f(x) = 5x³ + 5x² - 170x + 280 is (x + 7). What are all the roots of the function? Use The Remainder Theorem


Solution:

The all roots of the function ⇒⇒⇒ -7 , 2 and 4

See the attached figure for the detailed solution.

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The base of an aquarium with given volume V is made of slate and the sides are made of glass. If the slate costs seven times as

lubasha [3.4K]

Answer:

$l = \sqrt[3]{\frac{2V}{7}}$ $b = \sqrt[3]{\frac{2V}{7}}$ $h = \sqrt[3]{\frac{49V}{4}}$

Step-by-step explanation:

Represent the volume of the box with V and the dimensions with l, b and h.

The volume (V) is:

$V = l * b * h$

Make h the subject of the formula

$h = \frac{V}{lb}$

The surface area (S) of the aquarium is:

$S = lb + 2(lh + bh)$

Where lb represents the area of the base (i.e. slate):

The cost (C) of the surface area is:

$C = 7 * lb + 1 * 2(lh + bh)$

$C = 7lb + 2(lh + bh)$

$C = 7lb + 2h(l + b)$

Substitute $\frac{V}{lb}$ for h in the above equation

$C = 7lb + 2*\frac{V}{lb}(l + b)$

$C = 7lb + \frac{2V}{lb}(l + b)$

$C = 7lb + \frac{2V}{b} + \frac{2V}{l}$

Differentiate with respect to l and with respect to b

$C_l=7b - \frac{2V}{l^2}$ $=0$

$C_b=7l - \frac{2V}{b^2}$ $=0$

To solve for b and l, we equate both equations and set l to b (to minimize the cost)

$7b - \frac{2V}{l^2}=7l - \frac{2V}{b^2}$

$7l - \frac{2V}{l^2}=7b - \frac{2V}{b^2}$

By comparison:

$l =b$

$C_l=7b - \frac{2V}{l^2}$ $=0$ becomes

$7l - \frac{2V}{l^2}=0$

$7l = \frac{2V}{l^2}$

Cross Multiply

$7l^3 = 2V$

Solve for l

$l^3 = \frac{2V}{7}$

$l = \sqrt[3]{\frac{2V}{7}}$

Recall that: $l =b$

$b = \sqrt[3]{\frac{2V}{7}}$

Also recall that:

$h = \frac{V}{lb}$

$h = \frac{V}{\sqrt[3]{\frac{2V}{7}}*\sqrt[3]{\frac{2V}{7}}}$

$h = \frac{V}{\sqrt[3]{\frac{4V^2}{49}}}$

Apply law of indices

$h = \sqrt[3]{\frac{49V^3}{4V^2}}$

$h = \sqrt[3]{\frac{49V}{4}}$

The dimension that minimizes the cost of material of the aquarium is:

$l = \sqrt[3]{\frac{2V}{7}}$ $b = \sqrt[3]{\frac{2V}{7}}$ $h = \sqrt[3]{\frac{49V}{4}}$

8 0

2 years ago

Consider the following formula used to estimate height, h, of a seedling after w weeks since planting:

svp [43]

Answer:

Option B. $w=5h-8$

Step-by-step explanation:

we have

$h=(\frac{1}{5})w+(\frac{8}{5})$

Solve for w

That means ----> isolate the variable w

Multiply by 5 both sides to remove the fraction

$5h=w+8$

subtract 8 both sides

$5h-8=w+8-8$

$5h-8=w$

Rewrite

$w=5h-8$

4 0

2 years ago

A jar contains black marbles and green marbles. Sixty percent of the marbles in the jar are green. A number generator simulates

grigory [225]

Answer: D

Step-by-step explanation:

The number generator is not fair, in most of the experiments, considerably less than 60 % of the selected marbles are green.

And if Sixty percent of the marbles in the jar are green. A number generator should simulates randomly by selecting atleast one of the 60% of green marbles from the jar

5 0

2 years ago

If the 180 food calories found in a granola bar come entirely from p grams of protein, f grams of fat, and c grams of carbohydra

Mice21 [21]

f = 180 - p - c

to find the amount of fat subtract the protein and carbs from the original 180 calories

3 0

2 years ago

Read 2 more answers

Find the length of the longest line segment that can be drawn on a rectangular board 3.07m by 2.24m

nikklg [1K]

For rectangle
l=3.07m
b=2.24m
so longest side that can be drawn is diagonal of rectangular board
=squareroot l^2+b^2
=squareroot3.07^2+2.24^2
=squareroot9.4249+5.0176
=squareroot14.4425
=3.80
So longest line that can be drawn in rectangular board is 3.80m

3 0

2 years ago